I have not explored the PSTricks' pst-solides3d, TikZ's equivalent packages, Asymptote as a tool, etc, yet.

I have a task to make some simple 3D diagrams that are related to 3D geometry subject we learnt in senior high school. For example, we need to find the cross section of a cube cut by any plane, or a point at which a line penetrate a plane, etc.

Asymptote is not a package but it's surely the best tool to create complicated drawings in 3D. Now it's impossible to compare a tool like asymptote with a package like tikz. The first is a drawing tool and the second a fine package to illustrate some results. The choice depends on what you want.
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Alain MatthesOct 29 '12 at 7:22

1 Answer
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You mention that you've been tasked with drawing simple 3D structures. For that, a visually intuitive tool is Google Sketchup. 3D geometry for cubes is obtained by extruding (using the Push/Pull tool) a square, and model components can be intersected with one another.

Geometric perspective to the desired viewpoint is easily achieved via the orbiting tool. Print to PDF provides a means to include the resulting 3D structure to be included into your LaTeX document:

More complex figures and intersections are also possible using basic constructions of rectangles/circles and extrusions in 3D. Here the two pieces from the intersected cube has been separated: